4 papers
Mean-field theory via dissociated arrays for particle systems interacting through noisy weights
Nicolas Fournier, Datong Zhou
We study a mean-field limit for a -particle system in which each particle follows a diffusion and interacts with other particles through a weight on each directed edge. Each wei…
Dense networks of integrate-and-fire neurons: Spatially-extended mean-field limit of the empirical measure
Pierre-Emmanuel Jabin, Valentin Schmutz, Datong Zhou
The dynamics of spatially-structured networks of interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is kn…
The mean-field Limit of sparse networks of integrate and fire neurons
Pierre-Emmanuel Jabin, Datong Zhou
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuou…
Discretizing advection equations with rough velocity fields on non-cartesian grids
Pierre-Emmanuel Jabin, Datong Zhou
We investigate the properties of discretizations of advection equations on non-cartesian grids and graphs in general. Advection equations discretized on non-cartesian grids have re…